Should we Speak in Tongues in a Mixed Gathering?

A brief chat:

Him: I don't believe we should allow tongues in our church services, because Bible said if you speak in tongues and one who is unbeliever comes in, how will he cope?

Me: No! What Paul actually said is that you should interpret your tongues for him, and not that you should not speak in tongues at all

Him: And when we cannot interpret, we shut up?

Me: No! You don't shut up! You keep speaking in tongues to yourself. He never said keep shut. Let me show you

1Co 14:28  But if there be no interpreter, let him keep silence in the church; and let him speak to himself, and to God.

Let him keep silence IN THE CHURCH
... AND LET HIM SPEAK TO HIMSELF...

It is TO the church you keep silent. To yourself and to God, you continue to speak in tongues. Paul never stopped people from speaking due to inability to interpret.

In fact, he says,  "Wherefore let him that speaketh in an [unknown] tongue pray that he may interpret." 1Co 14:13.

You keep praying so you can interpret. Stopping will never make you do.
The moment you start to interpret, you qualify to speak TO THE CHURCH. You don't shut your mouth because there are some guys around who will say "you're mad". Rather, Paul taught that that is the more reason to get them to confess the Lordship of Jesus WHEN YOU INTERPRET

1Co 14:23-25 AMP
(23)  Therefore, if the whole church assembles and all of you speak in [unknown] tongues, and the ungifted and uninitiated or unbelievers come in, will they not say that you are demented?
(24)  But if all prophesy [giving inspired testimony and interpreting the divine will and purpose] and an unbeliever or untaught outsider comes in, he is told of his sin and reproved and convicted and convinced by all, and his defects and needs are examined (estimated, determined) and he is called to account by all,
(25)  The secrets of his heart are laid bare; and so, falling on [his] face, he will worship God, declaring that God is among you in very truth.

Paul only emphasized the place of interpretation for the sake of edifying the church IF IN A MIXED GATHERING, he never placed a ban on speaking in tongues

1Co 14:39 BBE So then, my brothers, let it be your chief desire to be prophets; but let no one be stopped from using tongues.

1 Cor 14:39 TLB
39 So, my fellow believers, ...never say it is wrong to "speak in tongues";