Yes, believers should most definitely invite unbelievers to church. Church should be a place where they can come and hear the preaching and teaching of the word of God.
Romans 10:14, "How then shall they call upon Him in whom they have not believed? And how shall they believe in Him whom they have not heard? And how shall they hear without a preacher?"
However, the church is not the only place where they can hear the word of God. All Christians should be able to accurately communicate the gospel message to unbelievers. People don't have to go to church for that. But, a good Christian church should naturally be a place where unbelievers should feel welcome and able to hear the truth of God's word. The Christians in such churches should make everybody feel welcome and comfortable. It's just being polite and showing proper Godly behavior.
Now, of course, there are churches that I would not recommend having unbelievers attend. There are churches that have overly charismatic behavior that looks like crazy people running around acting strange, talking in tongues, and generally being disorderly. This is not a good environment for unbelievers.
1 Corinthians 14:23, "If therefore the whole church should assemble together and all speak in tongues, and ungifted men or unbelievers enter, will they not say that you are mad?"
The above verse talks about a charismatic gift (tongues) being used in the church. Paul is concerned with how the unbeliever will perceive the assembly and so Paul requires order, not chaos. Tongues need to be practiced carefully, with sobriety and wisdom, so not to stumble unbelievers who may be attending.
Nevertheless, if a Christian church is Biblical it will not be chaotic, not misuse the charismatic gifts, will not always be begging for money, etc. Instead, it will preach Christ and him crucified in all of its messages. In other words, Christian churches need to preach who Jesus is and what he's done on the cross, and the gospel should be present in one form or another in all preaching.