Transversely isotropic (TI) models have become standard in depth imaging and are often used in waveform inversion. Here, we develop a robust wave-equation-based tomographic algorithm for building acoustic VTI (transversely isotropic with a vertical symmetry axis) velocity models from P-wave surface reflection and vertical seismic profiling (VSP) data. Wavefield extrapolation is performed with an integral operator to avoid generating shear-wave artifacts. Focusing energy in extended images produced by reverse-time migration (RTM) makes it possible to update the zero-dip NMO velocity Vnmo and the anellipiticity parameter η. To constrain the anisotropy coefficient δ and improve the accuracy in Vnmo and η, we employ borehole information by introducing an additional objective-function term designed to fit VSP data. Image-guided smoothing is applied to both data- and image-domain gradients to steer the inversion towards geologically plausible solutions. Testing on the VTI Marmousi model shows that the joint inversion of surface and VSP data helps estimate all three relevant medium parameters.