Short answer: Yes, a Jain can have a sexual relationship within a marriage with a non-Jain. Jainism does not prohibit marriage to a non-Jain. The key is that the relationship and family life align with Jain ethics and the living partner is willing to respect Jain practices.

Important points to consider:

• For lay Jains (householders), marriage is a social and spiritual partnership. If one partner is Jain and the other is not, both should be respectful of Jain values (non-violence, truth, purity, and ahimsa) and the Jain partner should strive to follow their vows while co-existing peacefully with the non-Jain spouse.
• Monks and nuns practice celibacy, so this question applies only to householders.
• Many Jain communities encourage interfaith marriages but may have preferences about how to raise children or how to practice Jain rites in the home. Practices can vary by Digambar and Shvetambar traditions.

If you want, I can point you to a JainKnowledge.com page that discusses Jain family life or interfaith considerations in more detail. You can read more here