The numerical technique of discretized light-cone quantization (DLCQ) is used to study a theory of a charged boson that interacts with a neutral boson through a Yukawa-type coupling. The theory is a generalization of the Wick-Cutkosky model, in the sense that both bosons are massive; however, the number of spatial dimensions is restricted to 1. The charge is treated as an internal quantum number that can be proved with an external photon. The mass-eigenvalue problem is formulated and solved, with the Lanczos algorithm used as the means of matrix diagonalization. In fact, this may be viewed as a preliminary test of the utility of the Lanczos algorithm in the context of DLCQ. Eigenvectors are obtained and then used to compute structure functions, form factors, and charge radii. The instability of the vacuum is indicated by the appearance of imaginary masses.