I am no expert but my understanding (according to my experience):

• One can not have his/her spouse on his/her plan if his/her spouse is offered coverage though his/her employer.
• I had my wife on my plan when she was unemployed. But when I applied to remove my wife from my plan (after she got a job), HR folks asked me to sign a paper stating reason. I don't remember disclosing her job details though.
• You can always change the coverage the way you like on qualified events (change of employment status of you or your spouse and open enrollment period).