I talked to my husband about this, asked him his opinion. He was thinking in different ways. He said that he (my husband) will often click away a page as I enter the room because at first he's not sure it's me, and it could be difficult child 3 (who shouldn't see some of the things husband digs up). The problem with this theory, I said, is the rubbish you're beginning to get, Then husband asked if it's possible that your girls are sneaking in to use the computer to access stuff like chat rooms. A lot of stuff the kids like to access will also lead right to the wrong sort of garbage landing in your computer.
If you think your girls could be part of the problem, then you could track them. But be aware, you will catch EVERYONE who is using the computer. Including your husband.
My husband also suggested - don't get the spyware that takes a snapshot of the screen, because each snapshot is a large graphic and it will quickly load up your computer and slow it down noticeably. You need to have a lot of space and a fast computer, plus check it VERY often, to sneak this one past.
Other spyware that husband suggested - you would need to set it up with a password for every family member. They would know you're doing something, if you do this, but it would also help you identify who it is that is deleting the history and cookies. It may not be husband. Or, it may not be ONLY husband. But whoever it is, they would probably become more cautious as a result.
There is a way to sneakily check - a key logger would do it, but without individual accounts (which would require their knowledge and cooperation) you would have to do some guessing as to who was home at the time to have access, sort of thing. But if you're a smart cookie, a key logger can show you individual patterns in key strokes, passwords, spelling errors and corrections, that sort of personal idiosyncrasy. husband set a trap for someone illegally using his work computer, and coincidentally discovered a few things about his co-worker (who also had use of the same computer) that he had to keep quiet. Yes, he got the bad guy too.
I know that when we've been thinking about what your husband may be up to, we've all been thinking "SEX!" but my husband suggested it could be gambling. It could be lots of things. Could he be planning a second honeymoon as a surprise? Mind you, the gambling would worry me far more than just about ANY sex. It's a lot harder to lose the house if he's just looking for sex.
Whatever you choose to do, think about it carefully and decide how you will handle any information you find. Also, you know your husband best, but where possible I always try to work with as much communication as possible. Who knows? If you talk to him and he's up to something, he may wake up to himself and stop. Or he might continue, but be more cautious. From the sound of things, he's not cautious enough now, for increased caution to make his actions undetectable if you try talking first then think you have to spy deeper.
Or husband may not be the only member of the household using the computer in this way.
You could instal a spy camera where it can videotape the computer screen, as well as who's using it. Be aware that a computer screen wouldn't show up too well on video (lines flashing across it on the tape) if it's out of sync. You could get a broad idea though, especially if there's sound. Don't run it off the computer though, and don't have the recorder unit itself in the same room (so the VCR drive motor won't be heard). Just record it to tape, check your tapes on fast forward for the periods of concern, then make further decisions. It may be the simplest option. But can you cope with your findings?
I might have to stop discussing this now, I think my husband is starting to get nervous! (just kidding; actually, I suspect I'm giving HIM ideas!)
Marg