Hola Jim

When we use "mientras" meaning "while" as in two actions happening at the same, we don't use "que"  (this is in Spain, but in Latin America mientras que is also sometimes used with this meaning)

Ella fregaba los platos mientras él veía la televisión. 

She washed the dishes while he watched TV.

(two simultaneous actions) 

However with the other meanings of "mientras", when you are making a "contrast" (whereas) or when we talk about a "condition" (as long as), the use of "que" is optional:

Mientras (que) mi hijo se portó bien, sus amigos interrumpieron todo el tiempo.

While my son behaved well, his friends interrupted all the time. (=whereas his friends...) 

Te invito a un café mientras / mientras que me ayudes a estudiar después.

I'll buy you a coffee as long as you help me study later.

Here are some Kwiziq lessons with different uses of mientras(que) if you'd like to see more examples for each use:

mientras with presente indicativo or presente subjuntivo

mientras que/en cambio for comparison/contrast 

See also this explanation given to this difference of mientras and mientras que (in Spanish) 

I hope it helps.

Saludos

Inma