We simulate selective A1BA2-A and A1BA2-B triblock solutions (that is, mixtures of the A1BA2 triblock with a solvent of either type A or type B) using a lattice Monte Carlo method. Although the simulated triblock chains are compositionally symmetric in terms of the A to B volume ratio, the A1 block is significantly shorter than the A2 block. For the pure A1BA2 melt the phase behavior is relatively well known, including the existence and stability of the recently discovered interstitial micelles which were found at the very strong segregation limit. In this paper, we investigate the stability of the interstitial micelles as a function of triblock volume fraction in a selective solvent of either type A or type B. The main finding of this paper is that adding a selective solvent of type A shifts the stability of the interstitial micelles into significantly higher temperatures which may provide a pathway towards experimental studies of interstitial micelles in real triblock solutions. We also find that adding selective solvents to the A1BA2 melt gives rise to a variety of nonlamellar nanostructures for temperatures and compositions at which the interstitial micelles are stable.