I have burning during sex & I noticed a brown discharge. What could this be? My husband and I have been checked for STDs & monogamous.

Vaginitis. Inflammation of the vagina is frequently not an infection. You may have hormones slightly out of balance, like occasionally happens on certain birthcontrol pills. You may have allergies to something your in contact with or even something your partner is in contact with. Cervical changes may give the discharge, again without an infection.
Possibly yeast. One of the very most common reasons for pain with intercourse is a vaginal yeast infection. After menopause, vaginal atrophy is a common cause for pain with sex, and that condition also greatly increases the risk for vaginal yeast infections as well - which will contribute to the pain. Both are easily treated once an accurate diagnosis is made, which will require an exam by your doctor.