Enriching bread with functional ingredients is a promising strategy to enhance the nutritional and bioactive profile of widely consumed foods. This study evaluated partial substitution of wheat flour (WF) with chestnut flour (CF) and rosehip powder (RP) on bread nutritional quality, functionality, and rheology. Five bread formulations were developed by replacing WF with CF at 0%, 5%, 10%, 15%, and 20%. Four other formulations were prepared by replacing WF in the 15% CF sample with RP at 0.5%, 1%, 2%, and 3%. Proximate composition, total phenolic content (TPC), total flavonoid content (TFC), antioxidant activity (DPPH and FRAP), and key physical characteristics were assessed, alongside the retention rates of functional attributes after baking. Rheological behavior of composite flours was analyzed using the MIXOLAB system to evaluate dough performance. Results showed that moderate WF substitution with CF (5–15%) increased dietary fiber and antioxidant activity while maintaining acceptable dough rheology and bread quality. At 20% CF substitution, TPC, TFC, FRAP, and DPPH increased 1.62-, 1.63-, 2.93-, and 3.03-fold versus control, with 59–66% retention. Addition of RP up to 3% to the 15% CF-substituted sample further enhanced bioactive properties, with TPC, TFC, FRAP, and DPPH reaching 2.13-, 2.03-, 4.49-, and 3.99-fold vs. BCF15, while retaining 61–67% of their functionality. Further inclusion of RP up to 2% in the 15% CF formulation maintains acceptable dough and bread performance, while 3% RP maximizes phytochemical enrichment but slightly affects technological properties. The combination of 15% CF and 2% RP provided a balanced enhancement in bioactive content and technological performance, offering a practical approach for producing functional bread with improved nutritional and technological attributes.