The modeling of nuclear reactors involves the solution of a multiphysics problem with various time and length scales. Mathematically, this requires solving a system of coupled, nonlinear, stiff, Partial Differential Equations (PDEs). This paper deals with the verification aspects associated with a multiphysics code, i.e., the substantiation that the mathematical description of the multiphysics equations are solved correctly (in time and space). Multiphysics applications have the added complexity that the solution field participates in various physics components, potentially yielding spatial and/or temporal coupling errors. We present a multiphysics framework that tightly couples the various physical models using the Jacobian-free Newton-Krylov technique (JFNK) and show that high-order convergence can be achieved in both space and time. Code verification results are provided.