Thanks for your questions, HPV infections can be confusing for women and I want to add a couple of things to Pat's great information.
First of all there is no test for HPV in men. I wish there were but currently only women can be tested through pap screenings and the HPV DNA probe.
Like Pat wrote, HPV has hundreds of different variants and only some of them are associated with cervical dysplasia and cervical cancer. We call those strains of HPV "high risk". It sounds like that is what you have and I am glad you are receiving the appropriate treatments from your doctor.
Your question about passing it to your partner and then getting reinfected is probably one of the most common questions I get from women about HPV. The simplest answer is that because HPV is a virus you will always have it, even if your cervical cells are not expressing dysplastic changes. If your partner has HPV and you have unprotected sex you are exposing yourself to whatever strain he has and you are exposing him to whatever strain you have. You cannot be reinfected with the same strain but you can be infected with other strains that you do not already have.
If you use condoms as protection they are only 70% effective against HPV infection because the virus often live on the scrotum in males.
Hope that helps and take care