We present a theoretical model for aqueous solutions of double-stranded (ds) DNA with explicit consideration of electrostatic interactions, excluded-volume effects, van der Waals attractions, and salt ions. With reasonable parameters estimated from the DNA structure and experimental data for electrolytes, we are able to reproduce the DNA osmotic pressure in the bulk in good agreement with experiment. The predicted DNA osmotic pressure in lambda-bacteriophages is found to coincide with that of the PEG8000 solution that inhibits DNA ejection as reported in recent experiments. Based on the radial distributions of DNA segments and of counterions at different degrees of packaging, we find that in the presence of Mg(2+), DNA forms a multilayer structure near the inner surface of a fully loaded bacteriophage, but at low packing density the DNA segments are depleted from the surface owing to the local condensation of DNA induced by the divalent counterions. By contrast, the multilayer DNA structure is less distinctive in the presence of Na(+) despite the increase of the DNA density at contact, and the depletion near the capsid surface is not found at low packing density.