Even people who care about kashrut sometimes find it challenging to manage. Asking someone who is not invested in it to maintain a kosher kitchen is, I suspect, very unlikely to work out, no matter how much good will the people start with.
In my marriage we have different opinions about kashrut, and what we decided was that, since I care more, I own the kitchen -- and what either of us eats outside of the house is our own business. I recommend a similar approach here: the one who cares about kashrut should do or oversee all the shopping, cooking, and cleaning in the kitchen, and the one who doesn't care should eat out sometimes to "get his fix" of bacon cheeseburgers etc. This may mean eating separately sometimes. If you had a completely separate kitchen that could work, but that's pretty uncommon and you still have to be careful that utensils, serving dishes, etc don't migrate.
Finally, a word of caution: kashrut is unlikely to be the only source of conflict in a mixed marriage. Have they talked about Shabbat? Pesach? Sukkot ("you want me to eat and sleep in a what?")? Family purity? How any children will be raised? A Jew considering marriage to either a non-Jew or a Jew with a drastically different observance level really needs to have a conversation with a trusted rabbi.
