Biden is absolutely a liberal.

Liberalism is a political and moral philosophy based on the rights of the individual, liberty, consent of the governed, political equality, right to private property and equality before the law. Liberals espouse various views depending on their understanding of these principles but generally support private property, market economies, individual rights (including civil rights and human rights), liberal democracy, secularism, rule of law, economic and political freedom, freedom of speech, freedom of the press, freedom of assembly, and freedom of religion, constitutional government and privacy rights.