We experimentally generate arbitrary time-bin qubits using continuous-wave light. The advantage unique to our qubit is its compatibility with deterministic continuous-variable quantum information processing. This compatibility comes from its optical coherence with continuous waves, well-defined spatio-temporal mode, and frequency spectrum within the operational bandwidth of the current continuous-variable technology. We also demonstrate an efficient scheme to characterize time-bin qubits via eight-port homodyne measurement. This enables the complete characterization of the qubits as two-mode states, as well as a flexible analysis equivalent to the conventional scheme based on a Mach-Zehnder interferometer and photon-detection.