By coherently combining advantages while largely avoiding limitations of two mainstream platforms, optical hybrid entanglement involving both discrete and continuous variables has recently garnered widespread attention and emerged as a promising idea for building heterogenous quantum networks. Different from previous results, here we propose a new scheme to remotely generate hybrid entanglement between discrete-polarization and continuous-quadrature optical qubits heralded by two-photon Bell state measurement. As a novel nonclassical light resource, we further utilize it to discuss two examples of ways -- entanglement swapping and quantum teloportation -- in which quantum information processing and communications could make use of this hybrid technique.