Short answer: yes, the child can be Jain if they are raised and practice Jain principles; the religion of the child is not decided by the marriage alone.

Simple explanation:

• Jain identity is about faith and practice, not just birth. If a Jain family marries a Hindu and the child is brought up with Jain values, performs Jain rites, and follows ahimsa, vows, and other Jain practices, the child can be a Jain.
• If the child is raised in a Hindu environment and follows Hindu beliefs, then the child would be considered Hindu in practice.
• There is no universal rule that a mixed-marriage child cannot be a Jain. Communities may have opinions, but the core Jain teaching emphasizes individual conduct and spiritual progress.
• Digambar and Śvetāmbara traditions both recognize that Jain identity comes from following the Jain path, though there can be differences in ritual details between the two traditions.

You can read more about how Jainism treats interfaith/mixed marriages and the emphasis on practice over birth here