In most states, Adultery consists of illicit sex between your spouse and another person, or the obvious opportunity to have sex in certain situations. As an example, what you've outlined in your question might be considered adultery, however, there is no absolute proof of it actually happening, so he may have a defense to the case if you sued for divorce.
Check with a local divorce lawyer to see how your state defines adultery as it applies to situations like yours.
I am actually licensed in Maryland.
As far as text messages -- unless he keeps the incriminating evidence on his phone, most cell phone companies keep texts in their systems for a brief period of time. Therefore, you have to act quickly.
You asked about adultery in Maryland, not other states.
In Maryland, under § 16-6-19. Adultery is defined as the following:
"A married person commits the offense of adultery when he voluntarily has sexual intercourse with a person."
Of course, you have to have admissible evidence regarding adultery. If you don't have witnesses to support your assertion, you may consider hiring a private investigator.
In Maryland, adultery is not defined by statute. Historically, adultery was as act of voluntary sexual intercourse committed by a married man with a woman who was not his spouse. The burden for proving a spouse committed adultery is placed upon the complaining spouse, in this case--you. Obtaining direct evidence of adultery can be very difficult. Therefore, the use of circumstantial evidence is allowed to prove adultery but you must prove both a disposition to commit adultery by defendant and his paramour and the opportunity for them to commit the act. Proof of disposition to commit adultery is usually shown through conduct, with a public display of intimacy being the most obvious example. Proving the opportunity to commit adultery is easier, usually through examples of the two individuals being alone together.
Adultery remains a misdemeanor in Maryland, punishable by a $10 fine. Proving adultery can be very difficult. You should consult an experienced divorce attorney before deciding whether to pursue a divorce based upon your spouse's alleged adultery.