Why "no keyloggers"? Not sure what you meant by that.
You can do a reverse lookup on the cellphone by using a service like intelius.com. There is a small fee.
A good keylogger is eBlaster. It's easy to install, virtually undetectable, and you can set it up to send you e-mails, unbeknownst to your husband.
If you have access to his car, you can put a silent, GPS-enabled cellphone in his trunk, hidden. BoostMobile has cheap $40ish phones, and for another $5-$10/mo. you can get a GPS app called MapQuest FindMe, which allows you to track the phone's movement via the web. You can also set it up to send you e-mails when the phone gets within "X yards/miles" from a predetermined location that you give it (such as GF's address, once you find it out).
You can also use a voice-activated recorder (they're about $80, at CircuitCity or BestBuy type store), velcro'd underneath the front seat of his car.
The keylogger on his computer would be the best, as it would capture all of his keystrokes on his computer, including logon/passwords, such as e-mail, which then open up a treasure trove of additional intel.
Any way to get the detailed billing on his cellphone account?
You should check on which of these is legal in your jurisdiction before doing any of this (for example, where I live, the car stuff is perfectly legal so long as I own or co-own the vehicle; same for the computer), and I would also warn you, that it's NOT for the feint of heart! Seeing/hearing raw intel (such as your husband exchanging "ILYs" and talking about sex with his GF) is like a sledgehammer to your chest.