Smart contracts are self-governed computer programs that run on blockchain to facilitate asset transfer between users within a trustless environment. The absence of contract specifications hinders routine tasks, such as program understanding, debugging, testing, and verification of smart contracts. In this work, we propose a unified specification mining framework to infer specification models from past transaction histories. These include access control models describing high-level authorization rules, program invariants capturing low-level program semantics, and behavior models characterizing interaction patterns allowed by contract implementations. The extracted specification models can be used to perform conformance checking on smart contracts, with the goal of eliminating unforeseen contract quality issues.