Catalyzes the four-electron reduction of biliverdin IX-alpha (2-electron reduction at both the A and D rings); the reaction proceeds via an isolatable 2-electron intermediate, 181,182-dihydrobiliverdin. Upon overexpression in E.coli with PCB:ferredoxin oxidoreductase, CpeS and either CpcB or PecB permits synthesis of phycocyanin-coupled CpcB or PecB