The word 'serviceman' applies to both male and female members of the military, despite having 'man' in it. My sister is a serviceman in the air force.
Pro Tip 2/3
Respectful Context
'Serviceman' is often used in contexts where the person is being respected for their military service. We thanked the serviceman for his dedication to our country.
Pro Tip 3/3
Branch Specific
Specify the branch when possible, such as a 'navy serviceman' or 'army serviceman'. At the parade, we saw many army servicemen in uniform.