In this article, we consider two interesting classes of an infinite planar graphs (viz., the flower graph Sn = ℱn×3 and the graph Dn* , constructed using prism graph) and for these, we study a graph parameter, called the mixed metric dimension (MMD). We prove that both of these are the families of planar graphs with an unbounded and non-constant MMD. We also discuss the concept of an independent MMD and for these classes of infinite graphs, we show that the mixed metric basis set LM is independent. We also compare the results of MMD, with some of the already obtained results regarding the variants of metric dimension for these two planar graphs.