The answer is: yes and no. If you mean that you are culturally Hindu and Christian by faith, then yes. Many Christians in India do. Some St Thomas Christians have been known to say, “We are Christians in faith, Indian in citizenship, and Hindu in culture.”
But it is a fine line and carries some caste-related problems with it, as well as theological ones. Religiously, you cannot be both.
On the Hindu side, it is possible, since many Hindus worship multiple deities. I have known of Indians who were raised in Hinduism or Sikhism, who then converted to Christianity. There was no problem for them in their families as long as they continued to worship the family gods and participate in traditional religious ceremonies and celebrations.
But Christianity is intensely monotheistic. When they realized that worshipping the family idols violated their new faith and so stopped praying to them, there was an uproar in the household. Some were kicked out of the house suddenly.
That is a key difference between Hindu and Christian faiths: the former is polytheistic and, thus, somewhat tolerant of additional gods — that is, as long as they are added and not substituted. The latter is monotheistic, which means that only that one god may be honored, so that really doesn't work. There is a conflict between the two, requiring individuals to make a choice.
So ... you can potentially be two religions if both are polytheistic (as with Hinduism) and / or universalist (as with Sikhism). But you cannot combine a polytheistic and monotheistic religion (or two monotheistic ones, like Christianity and Islam) without violating a core belief of at least one of those religions.
Quite simply, a monotheistic religion like Christianity, Islam, Judaism, or perhaps Zoroastrianism cannot allow worship of any additional gods or goddesses and remain monotheistic. It would have changed into a completely different religion, or been absorbed into its polytheistic counterpart.