@TedMullins having a female friend of your partners over for dinner is in no way comparable to having a person he misses working in your home, sharing a room, several days a week because he misses said person.
A one off normal social gathering does not compare in any way to a regular multiple weekly occurrence in the OP's home.
It is highly likely he does have feelings for her, even if he isn't fully aware of them himself and has even admitted it to himself.
Up to you OP if you want to accept this.
I think you should tell him that he should have her call over after work to hang out but that a shared work space several times a week in your home is not on.
Let them meet for coffee during work hours if he is so desperate to see her.
It really is ok to feel uncomfortable and to decide that this relationship isn't for you.
He misses her and that is not something that a lot of partners would feel comfortable hearing.
He has deep feelings for her, to miss her, IMO.