We performed a series of high-resolution simulations designed to study the substructure of Milky Way-size galactic halos (host halos) and the density profiles of halos in a warm dark matter (WDM) scenario with a non-vanishing cosmological constant. The virial masses of the host halos range from 3.3 x 10^12 to 1.7 x 10^12 solar masses and they have more than 10^5 particles each. A key feature of the WDM power spectrum is the free-streaming length R_f which fixes an additional parameter for the model of structure formation. We analyze the substructure of host halos using three R_f values: 0.2, 0.1, and 0.05 Mpc and compare results to the predictions of the cold dark matter (CDM) model. We find that guest halos (satellites) do form in the WDM scenario but are more easily destroyed by dynamical friction and tidal disruption than their counterparts in a CDM model. The small number of guest halos that we find within the virial radii of host halos at z = 0 in the WDM models is the result of a less efficient halo accretion and a higher satellite destruction rate. Under the assumption that each guest halo hosts a luminous galaxy, we find that the observed circular velocity function of satellites around the Milky Way and Andromeda is well described by the R_f = 0.1 Mpc WDM model. In the R_f = 0.1-0.2 Mpc models, the surviving subhalos at z=0 have an average concentration parameter c_1/5 which is approximately twice smaller than that of the corresponding CDM subhalos. This difference, very likely, produces the higher satellite destruction rate found in the WDM models. The density profile of host halos is well described by the NFW fit whereas guest halos show a wide variety of density profiles (abridged).