We present a novel interface for the exploration of multivariate data by integrating faceted search and interactive concept lattice visualizations. Concept lattices are Hasse diagrams showing hierarchical sub-concept relations in multidimensional data and result from a preceding Formal Concept Analysis. A concept lattice can be interpreted as the navigation space of exactly all possible results for a search that is based on conjunctive queries between terms. With Facettice we describe the two complementary visualizations Facet Lattices and Big Smart Lattice supporting interactive faceted search while visualizing and navigating in the concept lattice space. The design of our two visualizations is based on three integration goals which describe how faceted search can benefit from concept lattice visualizations and vice versa.