First of all, we show that two kinds of sandwich bilayers (BLs) are dynamically, thermally, and mechanically stable, which are degenerate p-type materials with intercalated Ca atoms, i.e., Nb-doped MoS2 homobilayers (HoBLs) and Nb-doped WS2-MoS2 heterobilayers (HtBLs) with 25% Nb content. Specifically, their interlayer bindings are five times stronger than van der Waals interactions in their pristine counterparts. Both of them are semiconductors with indirect band gaps in the visible region within the HSE06 exchange-correlation functional. Depending upon the presence and absence of centrosymmetry, they display interesting spin-valley coupling effects in such a way that opposite hidden spin polarization or opposite spin splitting is observed at opposite k-points. They can be easily engineered into direct gap materials under compressive (>2%) strain along the zigzag direction even with an explicit consideration of giant spin splitting. Under strain, they satisfy thermodynamic conditions for bifunctional catalysis in photocatalytic water splitting. In addition, the photoholes of the BLs can be subjected to lower overpotentials than those of pristine BLs for the oxygen evolution reaction. Electrons and holes in the sandwich HtBL can be separated into different layers under photon irradiation, allowing it to be more efficient than the corresponding HoBL in solar energy harvesting.