• We were between floors when the elevator broke down. [i.e. not specific and plural]

No the. idiom: to be between two things in the plural.

However, if you then want to be specific, you would say:

• We were between floors 2 and 3 when the elevator broke down.

BUT:

We were between the 2nd and 3rd floors when the elevator broke down.

• We were between two jobs when we got the call.
• We were between two major highways on a side road.

A plural noun after between does not require the before the noun.

However, you could say: We were between the two floors [if the floors have already been mentioned; the floors in question] when the elevator broke down.

• We were between floors when the elevator broke down. [i.e. not specific and plural]

No the. idiom: to be between two things in the plural.

However, if you then want to be specific, you would say:

• We were between floors 2 and 3 when the elevator broke down.

BUT:

We were between the 2nd and 3rd floors when the elevator broke down.

• We were between two jobs when we got the call.
• We were between two major highways on a side road.

A plural noun after between does not require the before the noun.

However, you could say: We were between the two floors [if the floors have already been mentioned; the floors in question] when the elevator broke down.