Hi @Meg_B
My husband has a BPii diagnosis. I do not know if he has cheated but he has impulsively gone walkabout, each time becoming increasingly suicidal. When hypomanic he went on some dating websites.
To trust again is difficult, I have forgiven my husband and part of this to me means not becoming "historical" and bringing up these indiscretions.
Perhaps it was not so hard for me; after a serious attempt I had nothing but love and compassion for my man.
It took a while and finding a medication that kept him stable helped too.
This does not mean that I have my head in the sand. I am well aware he could relapse. While he is happy to actively engage in treatment and let me be involved in that process I will continue to support him. This is not always easy.
Seeing a counselor may help you with boundary setting. If he wants to rebuild trust, transparency is essential, I would not think it unreasonable for him to give you access to his phone, email etc.
I will tag you in some threads that may be of interest to you.
Darcy