An outcome-adaptive Bayesian design is proposed for choosing the optimal dose pair of a chemotherapeutic agent and a biological agent used in combination in a phase I/II clinical trial. Patient outcome is characterized as a vector of two ordinal variables accounting for toxicity and treatment efficacy. A generalization of the Aranda-Ordaz model (1981, Biometrika 68, 357-363) is used for the marginal outcome probabilities as functions of a dose pair, and a Gaussian copula is assumed to obtain joint distributions. Numerical utilities of all elementary patient outcomes, allowing the possibility that efficacy is inevaluable due to severe toxicity, are obtained using an elicitation method aimed to establish consensus among the physicians planning the trial. For each successive patient cohort, a dose pair is chosen to maximize the posterior mean utility. The method is illustrated by a trial in bladder cancer, including simulation studies of the method's sensitivity to prior parameters, the numerical utilities, correlation between the outcomes, sample size, cohort size, and starting dose pair.