I'd still invite him out, and give him the space to be an adult and make his own decisions.

At the end of both pregnancies I was keen for DH to get out as much as humanly possible because I knew it would be his last outing on his own for quite some time. He is an adult. He knows what he can and can't do, and still be a responsible husband, birth support person and father.

If DH didn't make it to the birth because he was at an event, it was DH's fault, and no one else's.
Totally agree with this