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 CALIFA survey . The mass profiles within 2 R _ { e } are constrained well with 1 \sigma statistical error of \sim 10 \% . The luminous and dark mass can be disentangled with uncertainties of \sim 20 \% and \sim 50 \% respectively . From R _ { e } to 2 R _ { e } , the dark matter fraction increases from 14 \pm 10 \% to 18 \pm 10 \% for NGC 4210 and from 15 \pm 10 \% to 30 \pm 20 \% for NGC 6278 . The velocity anisotropy profiles of both \sigma _ { r } / \sigma _ { t } and \sigma _ { z } / \sigma _ { R } 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 disks are predominantly made up of cold orbits only beyond \sim 1 R _ { e } , 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 , are verified by applying the model to mock data .