Inter-religion or inter-faith marriages are clearly not allowed in Hinduism. As per the rules and regulations of Hindu Caste System, the marriage should always take place between two people of the same caste or varna viz. "Brahmin, Kshatriya, Vaishya and Shudra". Not only this, the Manusmriti clearly orders Hindus to boycott couples who marry outside their religion as it is against the rules of Hinduism.
If you opt for the legal way, then nothing is impossible. Legally, India has a clear set of rules and regulations for an inter-religious marriage: the Special Marriage Act, 1954, under which a couple, no matter what their religion or caste can marry without getting converted into another religion.