Classifying countries as either capitalist or socialist really depends on your definition of the two. If by capitalism1 you mean absolutely free markets then no we aren't capitalist (but why not just say free market instead? why single out capital/invested wealth as a central tenant?). As far as I know, there are no countries which can be considered to have freed markets as their economies must not only be free of government intervention but also from the coercion of individuals. Government is useful to protect individuals from coercion by others but tends to overstep this duty and use its power to apply its coercive forces where they do not belong.
If you mean capitalism2 in the more traditional way as coined by socialists (An ideology which supports a socioeconomic arrangement in which a dominant class controls capital and exploits labour as a result of State privilege in violation of the free market.) then our economy is indeed capitalist and free market (as defined by a market free from government intervention) capitalism is an oxymoron. The economic arrangement of having workers earn a wage from owners of the means of production is not contractually agreed upon free of the influence of the State. The State interferes in the market when it upholds the workplace owner's private property claim. The place of work cannot be theirs by right as not only was the capital required to establish it collected by exploitative means secured by State privilege but the very land it is established on cannot be claimed by any natural right to personal possession (they did not create the earth they built their business on). This exploitative economic arrangement allows business owners to collect more and more capital so that they may continue growing their business for their own pursuits. Bigger businesses have greater capital to spend so that they may increase their chances of capturing a larger share of the market. Wal-Mart owns the capital necessary to expand and push out small businesses. Most businesses in a capitalist economy are required to exploit their labour so they can collect the capital necessary to compete with other businesses lest they are run out of business (they can not stop of their own accord, they are obligated to continue to put profits ahead of everything else due to the structural constraints of the capitalist economy). The result is a trend towards centralization of capital and the means of production into the hands of fewer and fewer individuals (the 20% vs the 80% becomes the 1% vs the 99% becomes the 0.1% vs the 99.9% etc). Centralized economies are naturally less competitive and prevent workers from collecting compensation for the full value of their labour. This is the economic arrangement of the super majority of all modern countries. China, although it is essentially fascist, is also a capitalist country as its State upholds laws which protect the private ownership of the means of production. Sweden and similar countries with comparatively heavy social welfare policies also fit this description.
If by socialism1 you mean regulated markets then most countries should be considered socialist and there is no contradiction in socialist capitalism2 (Again, why not just say regulated markets?). The economy is regulated by the government into rigged markets which primarily serve the individual interests of entrenched large business owners.
However, socialism and capitalism in their traditional senses are fundamentally opposed. Socialism2 originally referred to sets of ideologies which led workers to come into their own, free them from exploitation, and abolish class division (and I mean class as a relationship to the means of production, not as the colloquial term for socioeconomic status (SES) which is a measure of income, education, job status, etc. By working class I don't mean to make a differentiation between blue and white collar work but between the employee and the employer). In this sense of socialism, only Cuba (state socialist minus the fact that independent labour unions are prohibited by the Castro dictatorship. So much for worker control of the means of production and the abolishment of class division. Cuba can be seen to be state capitalist. The means of production are privately controlled by the Castro oligarchy.) even comes close to qualifying as socialist (such was Lenin's view of socialism, more specifically the transitory period from capitalism to communism, by his own account: "socialism is nothing but state capitalist monopoly made to benefit the whole people"... the plan was that a vanguard, a group with much more advanced class consciousness than the masses, would violently overthrow the ruling class and ascend as rulers of the State, which in Marxism and Leninism is simply seen as a tool used by one class to oppress another, themselves and use it to gradually eliminate the prior ruling class. Having eliminated class conflict, the State would become obsolete and would wither away by its own right and communism would then be free to come about. However, by preserving the existing social relations of capitalism, Lenin failed to bring about any true revolution in the Marxist sense and his ideology should be seen as a revision of Marxism advocating reform by violent means. His state monopoly capitalism left Russia vulnerable to the worst abuses of capitalism. Meanwhile, his vanguard faces many of the same challenges as a democratically elected social democrat/labour majority in bringing about socialism/communism by reform). Libertarian socialism is an alternative to state socialism and advocates that the State take a true laissez-faire policy in respect to the economy and allow all citizens to freely decide for themselves how they want to organize their economic relationships. Truly free economic association for all: the freed market.