This paper deals with the Lyapunov stability and input-output stability of switched systems and their feedback interconnections. Here, each element (subsystem) of the switched system is assumed to possess the 'mixed' property. The 'mixed' property is a combination of small gain and passivity/negative imaginary properties. A definition of dissipativity for switched systems is given, wherein each subsystem is assumed to be dissipative and has an independent storage function. It is shown that the feedback interconnection of two dissipative switched systems is dissipative, using which stability results for feedback interconnection of two switched systems with 'mixed'-property are given. The result obtained is illustrated through an example with supporting simulations. © 2017 IEEE.