I wish I knew what to say.
He could be entirely innocent.
He could be having a flirtation.
He could be having an affair.
The only way you will find out is to talk to him and lay it on the line if he isn't, he has to stop being so secretive and making you feel like he is cheating.
Remind him of what he has to lose and then back off. Let the dust settle and see what happens.
If he truly has nothing to hide and loves you, imo, he would stop all the suspicious behaviour.