Another way to look at this is that you are lucky he isn’t the sort of guy to nail your hips to the mattress while forcing you to scream daddy as your biological father shifts uncomfortably next to his morning coffee at the breakfast table.
Dude has normal boundaries, if one of you has a private place, that is where you should be staying. I’m honestly curious as to why you want him to stay at your parents place when he has a perfectly usable apartment for both of you.
He is the person with a home. If you want him as part of your household, you should consider moving in together in a place that doesn’t belong to your parents.
When you find someone to make a family with, you are making a new family. It is not functional long term to try to work him into your existing family like that. One woman’s comfortable monotony is another man’s perpetual guest status.
I think the more feasible version of what you want would be some sort of family vacation that he is invited along for, but even that needs to come with private space for the two of you each day. Neutral territory lets people build a new status quo, and your parent’s place isn’t neutral at all. I know this might all sound dramatic and insane right now, but I’m speaking from a lifetime of experience—putting him in your parents space for over 24 hours is going to create mental stress for him that will have an adverse effect on your relationship, especially if you don’t acknowledge his stress as valid.