I know some 'shy' type guys, that joined Toastmasters groups.... specifically in order to help them get more socialized and more comfortable with interactions. And, you would never think they were the types to join these groups, but they did. And it turns out that they REALLY enjoy it... because there are others there, just like them.
Even my Dad as a college kid, joined a club and he did so to enable him to become 'successful' personally. It is personal enrichment.
Next, your Hubby is your opposite. And also, not everyone, "enjoys' hanging out with co-workers, after hours. I personally do NOT. I like to separate my 'personal' life and my 'work' life. Blatantly.
Just talk with him about it. Nicely. Don't make him feel like a 3rd wheel. Men, are sensitive.
And no, I would not set him up on play-dates for him... that can be emasculating for him, and really embarrassing... and I would think, that no 'man' would want everyone to know his Wife is doing that.
He is the opposite of you. Don't make him feel odd about that.
Or maybe suggest he join special interest groups.... hobby groups. Those are real fun.
Next: Be REAL glad....your Husband is not a "partying" type Man.... and a bar fly and that he does NOT have party-hardy type friends. That... is not a fun Husband to have, nor one you want to have. At all.
Your Husband sounds great... just shy.
Its okay... but you can talk with him about it.
Maybe it does NOT bother him, but it makes 'you' feel awkward.....
Suggest the Toastmasters clubs... or a hobby group. Something HE enjoys.
all the best,
Susan