
"According to a recent review of multiple studies, heterosexual serodiscordant couples have an almost non-existent risk of HIV transmission if the HIV-positive partner has an undetectable viral load as a consequence of successful antiretroviral (ARV) therapy."
Also check out Shawn & Gwenn's YouTube - a mixed-status couple who vlog about their marriage & sexual issues.
Can people with HIV get married? Be intimate?

Yes, people living with HIV can marry, have normal sexual relationships and have children. (read more about reproduction here)
Having HIV does NOT prevent anyone from dating or marrying—it just may require a little more responsibility and trust from both people in the relationship. 1
A “mixed status” couple is one in which one partner is HIV-positive and the other is HIV-negative. (They are also referred to as serodiscordant couples.)
According to a recent review of multiple studies, heterosexual serodiscordant couples have an almost non-existent risk of HIV transmission if the HIV-positive partner has an undetectable viral load as a consequence of successful antiretroviral (ARV) therapy." 2
Obviously careful planning is required in regards to sexual relations, but reports indicate that latex condoms are highly effective in the prevention of HIV and other STDs when used consistently and correctly.
In spite of the challenges that exist in serodiscordant relationships, they can and do flourish. The fact of the matter is that, not unlike any relationship, it takes effort, communication and commitment from both partners.