Next-generation heterogeneous cellular network (HCN) expects more and more deployment of the base stations and spectrum to achieve data rate in gigabits per second with seamless connectivity. Recently, small cell deployment has proven its effectiveness for increasing the coverage and area spectral efficiency (ASE) of the cellular network. Although, dense small cell deployment also increases the deployment cost and cross-tier interference of the network. This paper suggests switching-based mixed millimeter wave (mmW)/ultra high frequency (UHF) cellular network as a possible solution to overcome these challenges. In mixed mmW/UHF cellular network (named as MMUCN), mmW is used as the main transmission link, and UHF band is utilized as a backup link. In this paper, a theoretical framework is developed using tools from the stochastic geometry to analyze the outage performance, ASE, and deployment cost efficiency (DCE) of the MMUCN, which comprises existing macro base stations and mmW base stations. Optimal mmW base station densities constraints by the outage are calculated, which maximizes the ASE and DCE. Furthermore, a multiobjective optimization problem is formulated to maximize ASE and DCE simultaneously. Numerical results show that MMUCN outperforms UHF-based two-tier cellular network and efficiently mitigates the cross-tier interference of the system.