The invention provides novel bispecific monoclonal antibodies carrying a different specificity for each binding site of the immunoglobulin molecule and methods for producing novel bispecific monoclonal antibodies carrying a different specificity for each binding site of the immunoglobulin molecule. The antibodies are composed of a single heavy chain and two different light chains, one containing a Kappa constant domain and the other of a Lambda constant domain. The invention provides methods for the isolation of antibodies of different specificities but sharing a common heavy chain. The invention also provides methods for the controlled co-expression of two light chains and a single heavy chain leading to the assembly of monospecific and bispecific antibodies. The invention provides a mean of producing a fully human bispecific and bivalent antibody that is unaltered in sequence and does not involve the use of linkers or other non-human sequences, as well as antibody mixtures of two monospecific antibodies and one bispecific antibody. The invention also provides the means of efficiently purifying the bispecific antibody.