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 $1sigma$ 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 $14pm10%$ to $18pm10%$ for NGC 4210 and from $15pm10%$ to $30pm20%$ 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.
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