Mixed-paradigm process models integrate strengths of procedural and declarative representations like Petri nets and Declare. They are specifically interesting for process mining because they allow capturing complex behaviour in a compact way. A key research challenge for the proliferation of mixed-paradigm models for process mining is the lack of corresponding conformance checking techniques. In this paper, we address this problem by devising the first approach that works with intertwined state spaces of mixed-paradigm models. More specifically, our approach uses an alignment-based replay to explore the state space and compute trace fitness in a procedural way. In every state, the declarative constraints are separately updated, such that violations disable the corresponding activities. Our technique provides for an efficient replay towards an optimal alignment by respecting all orthogonal Declare constraints. We have implemented our technique in ProM and demonstrate its performance in an evaluation with real-world event logs.