Utilizing Monte Carlo simulation techniques, we have calculated both the helicity modulus and heat capacity versus temperature of a coupled classical XY model in two dimensions. Our model system is based on a Hamiltonian first proposed by Bruinsma and Aeppli [Phys. Rev. Lett. 48, 1625 (1982)]. The helicity modulus results strengthen our previous report of a new type of phase transition in which two distinct types of order are simultaneously established through a single continuous transition.