Catalan first observed that the numbers S(m,n), now called the super Catalan numbers, are integers, but there is still no known combinatorial interpretation for them in general. Interpretations have been given for the case m = 2 and for S(m, m + s) for 0 ≤ s ≤ 4. In this paper, we define the super FiboCatalan numbers S(m,n)_F and the generalized FiboCatalan numbers. In addition, we give Lucas analogues for both of these numbers and use a result of Sagan and Tirrell to prove that the Lucas analogues are polynomials with non-negative integer coefficients. This proves that the super FiboCatalan numbers and the generalized FiboCatalan numbers are integers.