Depends. First, celphone record may or may NOT tell you anything. I had a number of calls on my celphone from my ex boyfriend after I was married, and that was because he had my office and I handle a business matter on the sale of a property he and his brother owned. Over the three months from offer to close, there were a numer of times phone contact was necessary. And phone contact was all there was-for business.
However, if the cel is provied by his employer, the bills are their property. In which case, I would presume it would take a court order. If it is his own bill and it comes to the house, he is not obligated, legally to share it with you. My DH has me handle payment on his cel phone, so I do the online payment and have all the logins to access the account. As it does not appear you do, try talking to him about it and ask to see the bill?