Summary: For a bisexual branching process in a random environment, the conditional mean growth rate per mating unit is introduced, and its related properties are studied. Then the upper and lower bounds of conditional mean of the process are obtained. The limiting behaviors of the number of mating units in each generation normalized by these two bounds are respectively investigated. Particularly, the limiting behaviors of the number of females and males in each generation normalized by slightly modified bounds are discussed too, and equivalence theorems between the normalized number of mating units and that of females or males in each generation are obtained.