I married a Methodist. But we were married by a priest, in a Catholic church, and went through the Catholic pre-Cana program.
I have a relative who married a Baptist. She wanted to get married in her home church, by her home pastor. I want to say they had a priest + the Baptist pastor conduct the ceremony. But later on, the marriage failed. The relative went through the annulment process. And even though they were gathering all sorts of evidence about emotional/psychological stuff, I think the key thing that the annulment went through on was the fact that the marriage hadn’t taken place in the Catholic church building (and was without the Catholic Mass?), and ergo, was not a sacramental marriage.
I could be wrong, and I’m sure someone will point it out.

But that’s the way the situation was explained to me.
–edit–
Thinking about it, I think one key element was that the priest was from the Diocese of X, where the priest had been assigned to my relative’s campus church, and the Baptist church where the wedding took place was in the Diocese of Y. So it may be that they hadn’t gotten the bishop’s permission, or perhaps the correct bishop’s permission, for the venue.
–edit again–
When you enter into a mixed marriage, you both promise to be open to children, and promise to raise them Catholic. So far, with the wedding plans, it doesn’t seem like the Catholic stuff is taking a very prominent role.

Do you expect that to suddenly change once children become involved?
Good luck figuring things out.

It’s not an easy thing. Hugs.