The transient excitation of two identical, straight, thin wire antennas above a plane interface between two homogeneous dielectric half spaces is analyzed. The two wires are located parallel to each other and to the interface, and one of them is excited by a voltage source. By applying symmetry considerations, the problem is decomposed into two single-wire problems, for which a method of solution is available from previous work by the authors [Rubio Bretones and Tijhuis, 1995]. The problem is solved in two steps. First, the configuration of two wires in a homogeneous medium is studied. The electric field integral equation for the total current on the wires is derived directly in the time domain and subsequently solved by using the continuous-time discretized-space approach. This results in a linear system of equations of a fixed dimension which is solved by marching on in frequency. Subsequently, we consider the complete configuration. As in our previous work, the field reflected by the interface is treated as a secondary incident field in the integral equation for the currents on the two wires. This leads to an integral equation of a form similar to the one describing the currents on the two wires in free space. In this equation the response of a pulsed dipole source in the two-media configuration occurs as a Green's function. The spatial Fourier inversion involved is carried out with the aid of a fixed composite Gaussian quadature rule. This again leads to a system of equations of a fixed dimension, which can be solved by marching on in frequency. Finally, some representative numerical results are presented and discussed.