This paper presents global solutions of adiabatic accretion flows with isothermal shocks in the potential of a non-rotating black hole. It is known that in the previously studied cases, where flow including shock is either entirely adiabatic or entirely isothermal, there can be no more than one stable shock solution, and the solution can only be of the a-x type; however, the solution topology in the present case shows new remarkable characteristics: for the same flow parameters there can be two stable shock solutions satisfying the physical boundary conditions, and the solution can be of three types, namely a-x, x-a, and a-a type. In addition, shocks in the present case occur for a parameter region that is different from that for RankineHugoniot shocks to occur. These results greatly increase the possibilities of shock formation in astrophysical flows. It is also noted that in the present case the efficiency of energy release at the shock can be as high as a few percent. Finally, a brief comparison is made between shocked inviscid flows and two types of shock-free viscous flow, namely that of Shakura and Sunyaev (1973, AAA 09.066.049) and that of Narayan and Yi (1994, AAA 61.064.083).