When implementing helicopter $\mathrm{-}$satellite communications, periodical interruption of the received signal is a challenging problem because the communication antenna is intermittently blocked by the rotating blades of the helicopter. The helicopter $\mathrm{-}$satellite channel model and the Forward Error Control (FEC) coding countermeasure are presented in this paper. On the basis of this model, Check-Hybrid (CH) Low-Density Parity-Check (LDPC) codes are designed to mitigate the periodical blockage over the helicopter $\mathrm{-}$satellite channels. The CH-LDPC code is derived by replacing part of single parity-check code constraints in a Quasi-Cyclic LDPC (QC-LDPC) code by using more powerful linear block code constraints. In particular, a method of optimizing the CH-LDPC code ensemble by searching the best matching component code among a variety of linear block codes using extrinsic information transfer charts is proposed. Simulation results show that, the CH-LDPC coding scheme designed for the helicopter $\mathrm{-}$satellite channels in this paper achieves more than 25% bandwidth efficiency improvement, compared with the FEC scheme that uses QC-LDPC codes.