We develop a numerical model that treats the three-dimensional (3-D) magnetohydrodynamic interactions taking place at interplanetary corotating stream fronts near the heliographic equator during those periods of the solar cycle when the large-scale coronal magnetic structure is in the tilted-dipole configuration. The dynamic simplicity of the tilted-dipole geometry permits the formulation of a local approximation valid over a limited range of heliographic latitudes and longitudes centered about the stream front. We show that one component of the spatial orientation of the stream interface is fixed by the implied coronal configuration and that this orientation varies in a systematic and predictable way with heliocentric distance. This is important, since the orientation of the interface regulates the pace of the interplanetary evolution by determining the obliquity of the dynamical interaction between fast and slow flows at the stream front. We find that the appearance of 3-D tilted-dipole interfaces near the Sun (0.3--0.6 AU) may differ considerably from the classic 2-D structures described previously in the literature; they should be subtle features, in which the amplitudes of the nonradial flow deflections are only a few degrees and the north-south component dominates the east-west component. In particular, we expect that the amplitude of the total nonradial deflection should go roughly as sin &agr; (where &agr; is the dipole tilt angle). whereas the ratio between the north-south and east-west deflections should vary as cot &agr;. We also show that magnetic torques should have strong influence on the interface structure near the Sun (inside ~0.5 AU); the amplitudes and phases of the nonradial flows there are subject to details of the large-scale magnetic properties of the flow, which can only be assessed observationally. In addition, magnetic stresses carried in the solar wind may inhibit the formation of discontinuous interfaces in this region. The effects of the tilted-dipole geometry on the evolution of corotating interaction regions and the formation of shocks at larger heliocentric distances will be addressed in a subsequent paper. ¿ American Geophysical Union 1991