Building height (BH) and building footprint (BF) jointly describe the vertical and horizontal extent of the built environment and are required inputs for urban climate, disaster-risk, and population-mapping models. The two parameters are coupled through floor-area-ratio (FAR) constraints, yet remote-sensing approaches typically treat them as independent regression targets. We argue that explicitly encoding this cross-task coupling is more impactful than further refining individual encoders, and propose MorphoFormer, a joint BH/BF estimation framework built around two complementary mechanisms: (i) a BF-Guided Task Decoder (BGTD) that gates the height branch via cross-attention on a footprint-derived morphology context, and (ii) a Morphology Consistency Loss (MCL) that supervises a height-from-footprint surrogate against the ground-truth BH, indirectly forcing the BF feature to encode height-correlated structure. The encoder is a single-stage Swin backbone fed by Sentinel-1 SAR, Sentinel-2 multispectral, and DEM inputs, trained and evaluated on a geo-blocked split of 54 cities. Against a Swin-MTL baseline at identical receptive field, MorphoFormer reduces BH test RMSE from 3.39 to 3.15 m (R^2 improves 0.62 -> 0.67) with BF R^2 stable at 0.80. Controlled ablations at identical capacity attribute most of this 0.24 m improvement to the two proposed mechanisms: removing BGTD raises BH RMSE by 0.11 m and removing MCL raises it by 0.11 m, with the residual approximately 0.02 m falling within the noise floor of encoder-side variations. Because both mechanisms act on cross-task representations rather than pixels, the design carries no intrinsic dependence on input resolution.