The purpose of this paper is to study the interaction between a two-level system (qubit) and two continuous-mode photons. Two scenarios are investigated: Case 1, how a two-level system changes the pulse shapes of two input photons propagating in a single input channel; and Case 2, how a two-level system responds to two counterpropagating photons, one in each input channel. The steady-state output field states for both cases are derived analytically in both the time and frequency domains. Numerical simulations demonstrate rich and interesting two-photon scattering phenomena induced by a two-level system.