What is the regular expression describing this language?
Yes, your idea is correct.
Basically here two things are happening.


Regular languages are closed under compliment operation
If L1 is accepted by DFA1 and DFA2 is obtained by interchanging the final states to non-final states and non-final states to final states of DFA1 then the language accepted by DFA2 is compliment of L1. That is, if


DFA1 is a quintuple (Q, Σ, δ , q0, F)
And L1 is language accepted by DFA1
DFA2 is (Q, Σ, δ , q0, (Q - F))
And L2 is language accepted by DFA2 Then L2 is compliment of L1.



In this case the languages L1 = {w∣w is any string except 11 and 111} and L2 = 
{v∣v is either 11 or 111} are compliment o each other .
Hence your approach is correct.