Canada/US spousal sponsorship simultaneously?

Hi,

My boyfriend lives in the US and I live in Canada. We are talking about getting married to start the process of spousal sponsorship. We're both employed, but mobile, and we don't have a preference for which country we want to settle in -- whichever is easier for both to live and work!

Is it possible for us to marry and for me to start the process of sponsoring him into Canada, while at the same time he starts the process of sponsoring me into the US?

WIll that cause any problems with our applications?

Also, we see each other about once a month right now, just driving across the border without any real hassles since at this point we only stay in the other's country about a week and then return home.

Can we still maintain our monthly visits while our visa applications are underway or will we get hassled by immigration officials who might be suspicious that we are trying to stay in the country illegally?

Thanks