A promising route to scale fault-tolerant quantum computers to practically relevant sizes is through a network of distributed matter-based quantum processing units (QPUs) connected by photonic links. While the matter qubits inside each QPU experience predominantly Pauli-type errors that are well handled by circuit-based quantum error correction (CBQC), the inter-node channel is dominated by photon loss and probabilistic linear-optical operations, which are better handled using measurement-based quantum computing (MBQC) and fusion-based quantum computing (FBQC). Yet MBQC and FBQC are usually treated as alternatives to CBQC, rather than as components that can be combined with it. Recent work uses the ZX-calculus to explicitly translate syndrome extraction circuits and their associated checks between CBQC, MBQC and FBQC, opening the door to protocols that mix paradigms within a single error-correcting code. In this work, we introduce hybrid error correction protocols for distributed quantum computing systems that combine CBQC with MBQC and FBQC. We show that a variety of protocols using linear-optical fusions for distributed lattice surgery attain a 50% threshold for loss-induced erasure at the interface, and that hybrid protocols built from linear resource states double the effective erasure distance at the interface on the observable measured in the merge while preserving it on the perpendicular joint observable – in contrast with standard approaches using Bell pairs or Bell state measurements for which the interface preserves only one of the two observables with no effective distance increase. We numerically evaluate the performance of these protocols under heterogeneous noise models that include local depolarising noise, loss, fusion failure, and resource state errors, verifying all predicted erasure thresholds are achievable and demonstrating that the augmented interface distance for hybrid lattice surgery leads to lower logical error rates under high loss rates.