Eventually, the child will, at their own discretion, choose which one they feel is correct, or they may decide to carry both in life. If not, the child may decide not to have any faith at all. Whichever the choice, they should not be scorned by either parent because of it.
It most certainly won’t be easy, but it is possible. Just as you were able to marry someone of a different faith without loving them less or feeling the need to convert them into your beliefs, the same should be for the child. While you may not be able to raise them directly under either faith, you both can (and probably should) teach your child of both faiths without tearing the others down, and show forgiveness if the child does something that is seen as normal for one of your faiths, but not the other. The child shouldn’t be pulled or tugged in either direction, or told that they are playing favorites with the parents if they choose not to follow one or the others faith.