Heat and mass transport in biological tissue are strongly influenced by local blood flow, vascular architecture, tissue composition, and physiological or pathological conditions. Accurately characterizing transport behavior in localized regions remains challenging due to the multiscale nature of the vasculature and the spatial heterogeneity of transport parameters. Conventional bioheat and mass transport models often simplify the vascular system by treating tissue as a homogenous continuum or porous medium, limiting their ability to capture localized vessel-tissue interactions. We propose a multiscale transport modeling framework to address these limitations. Larger vessels, where advection and direct exchange with surrounding tissue dominate transport, are explicitly modeled using one-dimensional flow and transport equations. Smaller vessels, where diffusion is the primary transport mechanism, are represented implicitly within the tissue continuum. The one-dimensional vascular and three-dimensional tissue transport models are explicitly coupled to ensure bidirectional exchange and strict conservation of energy or mass flux between domains. The proposed one-dimensional transport and multiscale transport models are validated through comparisons with analytical solutions and commercial solver results for idealized vascular configurations. Their performance is further evaluated against conventional bioheat transfer models, highlighting differences arising from explicit versus homogenized vascular representations. Finally, the multiscale framework is applied to localized tissue regions containing complex vascular networks to demonstrate its applicability under physiologically relevant conditions.