We study vortex structure in a two-band superconductor, in which one bandis ballistic and quasi-two-dimensional (2D), and the other is diffusive andthree-dimensional (3D). A circular cell approximation of the vortex lattice withinthe quasiclassical theory of superconductivity is applied to a recently developedmodel appropriate for such a two-band system (Tanaka et al 2006 Phys. Rev.B 73 220501(R); Tanaka et al 2007 Phys. Rev. B 75 214512). We assume thatsuperconductivity in the 3D diffusive band is ‘weak’, i.e. mostly induced, as is the case inMgB2. Hybridization with the ‘weak’ 3D diffusive band has significant and intriguing influenceon the electronic structure of the ‘strong’ 2D ballistic band. In particular, theCoulomb repulsion and the diffusivity in the ‘weak’ band enhance suppression ofthe order parameter and enlargement of the vortex core by magnetic field inthe ‘strong’ band, resulting in reduced critical temperature and field. Moreover,increased diffusivity in the ‘weak’ band can result in an upward curvature of theupper critical field near the transition temperature. A particularly interestingfeature found in our model is the appearance of additional bound states at thegap edge in the ‘strong’ ballistic band, which are absent in the single-band case.Furthermore, coupling with the ‘weak’ diffusive band leads to reduced bandgapsand van Hove singularities of energy bands of the vortex lattice in the ‘strong’ballistic band. We find these intriguing features for parameter values appropriate forMgB2.