Is it a good idea to host your husband’s female friend when you’re not around?

For some context, husband and I have been married just over a year and recently moved to a new area, very far from my family (who lived about an hour from us at our last place), for my new job. I work in person 8-5 everyday and since I just joined, I don’t have any vacation time yet. He works from home because his job allows it. We’re also still in the process of setting up our new home. Our marriage was troubled at the beginning but we have been in a good place the last few months.

Earlier today, hubby texted me at work saying that his friend might be visiting us next Wednesday, he didn’t specify who or how he knows her, just that it’s a her. By itself, not odd but he has a habit of over sharing whether the other person likes it or not so by his standards, weird. I told him that we should probably buy a mattress for the guest bedroom and asked if she’s only staying for that one day. He then comes back saying that he spoke to her and found out her parents and brother passed away last year, and she just went through a breakup, and he didn’t know what to say so he invited her to stay with us instead. He then answers my question saying that she’s likely staying for the entire long weekend (Independence Day falls on the Tuesday after the weekend, so he has Monday and Tuesday off, I work on Monday and won’t be home for a majority of the day). I was teasing him just last night that even though he has a long weekend, we won’t be able to go anywhere since I have work on Monday. Anyway, point is, essentially he’s telling me he invited his female friend to stay with us for a week without bothering to ask me or even letting me know before extending the invitation.

I completely understand that I sound like a jealous b**** right now but here are my concerns:

• I already see him being a bit secretive about who this person is, how he knows her, etc, which is very unlike him.
• he just extended an invitation to this person to come and stay with us for a week, over a weekend that we were both hoping would be relaxing, without so much as even asking me if it was okay.
• over the last few weeks, he has repeatedly complained that he misses me when I’m at work and feels like we don’t spend quality time together, but when I ask what he wants to do instead of watching tv in the evenings, he doesn’t know. I’ve tried to balance it out with some surprise outings and things are good on those days, but it’s not enough and there’s little to no effort from him to change it.
• our s*x life sucks. We’ve had ups and downs with it and there have been temporary reasons for it (I.e. periods, having to work late, something hurting, etc) but he did mention a few days ago that he feels s*xually frustrated. Now his newly single and likely very emotionally vulnerable female friend is coming over for a week and they will be alone for a majority of that time since I’ll be at work. It’s not that I don’t trust him but i know he has a hard time saying no to someone who’s close to him or is in a bad state. I also don’t know the friend, and people who are in a vulnerable state tend to look for comfort however they can get it.

feel free to tell me if you think my concerns are absolute BS or if you have any other advice/lessons from your own life to share. Also, please don’t get me wrong, I’m 100% down to help his friend in whatever way I can, I just can’t help but think that I’m inviting trouble into my life and marriage by hosting her.