Schwarzschild orbit-based dynamical models are widely used to uncover the internal dynamics of early-type galaxies and globular clusters. Here we present for the first time the Schwarzschild models of late-type galaxies: an SBb galaxy NGC 4210 and an S0 galaxy NGC 6278 from the Calar Alto Legacy Integral Field Area (CALIFA) survey. The mass profiles within 2Re are constrained well with 1σ statistical error of ∼ 10 per cent. The luminous and dark mass can be disentangled with uncertainties of ∼20 and ∼ 50 per cent, respectively. From Re to 2Re, the dark matter fraction increases from 14 ± 10 to 18 ± 10 per cent for NGC 4210 and from 15 ± 10 to 30 ± 20 per cent for NGC 6278. The velocity anisotropy profiles of both σr/σt and σz/σR are well constrained. The inferred internal orbital distributions reveal clear substructures. The orbits are naturally separated into three components: a cold component with near circular orbits; a hot component with near radial orbits and a warm component in between. The photometrically identified exponential discs are predominantly made up of cold orbits only beyond ∼1Re, while they are constructed mainly with the warm orbits inside. Our dynamical hot components are concentrated in the inner regions, similar to the photometrically identified bulges. The reliability of the results, especially the orbit distribution, is verified by applying the model to mock data.