The classical traffic assignment problem determines the equilibrium flows on a congested network with many infinitesimal users who choose paths to minimize their own travel times. Travelers care about cost (including tolls) as well as time, and different travelers put different weights on these two criteria. We study a bicriteria traffic assignment problem in which travelers differ in their tradeoff between a flow-independent cost, such as tolls, and a flow-dependent cost, such as travel time. Existing formulations require either finitely many user classes or positive preference densities, including formulations for positive preference densities that are either infinite-dimensional or nonconvex. We formulate a finite-dimensional convex optimization problem for arbitrary preference distributions with bounded support, including distributions with a mixture of atoms, densities, and gaps in their support, and we show how to convert an optimal solution to an equilibrium of the bicriteria traffic assignment problem. We propose an algorithm that alternates between solving a convex problem for a (typically small) number of paths, and solving a parametric shortest-path problem. Computational experiments on benchmark networks illustrate the performance of the algorithm relative to existing methods.