This paper proposes an analytical approach to modeling and analyzing the coexisting transmission performance in a multi-tier heterogeneous network with multiple radio access technologies (Multi-RATs). The coexistence issue is a special phenomenon uniquely existing in a multi-RAT network and it is rarely studied in prior works on heterogeneous wireless network. To simply characterize the coexisting transmission impacts in a multi-RAT network, in this paper we consider a three-tier heterogeneous network using the RATs of L and U, where RAT-L is adopted by the access points (APs) in the first two tiers, APs in the third tier only use RAT-U and the APs in the second tier can opportunistically use RAT-U. The opportunistic CSMA/CA protocol is used by the APs contending the RAT-U channel and the channel access probabilities for the RAT-U AP in two different tiers are derived under the proposed user association scheme with random weights. The coexisting coverages of RAT-L and RAT-U are defined and found, respectively. Numerical results show that the proposed modeling and analyzing approach can be well applied to evaluate the coexistence transmission performance while LTE and WiFi APs both access the unlicensed band.