Q: Help with airport extreme

Your problem can be in any of a number of places.

Sorry but details are important.. we cannot proceed without getting down to actual connections and wireless strength etc.

I take it the Belkin as main router is happily controlling the network.

The Extreme should be plugged in by ethernet to it.. and setup in bridge mode.

The Express could be either wired directly to the Extreme or using Extend Wireless mode which I am guessing is what you mean by bridge.

Now it is important to know exactly how everything here is setup.. so please make a couple of screenshots which you can post.. look particularly at the wireless link between the extreme and express.

Click on the wired Extreme and give me its summary page.. and then the one like mine.. roll the pointer over the connection: always Unknown since El Capitan. It will then bring up some more details of the link which is important.

If your computer is linking to the Belkin do not expect the airport to reliably show up. There are a number of reasons for this but one is local domain. Please set the Belkin to local if possible.. but even that is often not enough to get the Apple DNS working reliably.

Not sure I understand clearly what you are trying to accomplish.

The AirPort Extreme will need to connect to the Belkin router using a permanent, wired Ethernet cable connection. If you can locate the AirPort Extreme a few rooms away from the Belkin router, you can set up the Extreme to produce a wireless signal that uses the same wireless network name and password as the Belkin network.......so, you will have a "bigger" network.

Once the Extreme is set up and working, you can reconfigure the AirPort Express to wirelessly extend the signal from the AirPort Extreme, although it would be better if you could connect the Express back to the Extreme using a wired Ethernet cable connection.

Another option would be to connect both the Extreme and Express back to the Belkin router using a permanent, wired Ethernet cable connections.

If you were thinking of having the Extreme extend the Belkin wireless signal by connecting back to the Belkin using wireless, the Extreme would not be able to do this, nor would the Express.

I would strongly recommend you do a completely new configuration for the extreme. Factory reset and start over.

Using two different wireless networks is fine. But the wireless signal to the express so it can properly extend must be good or better.

Can't find a way to get the connection shot as I'm still using 10.9.5.

Just open your airport utility.. it makes no difference which OS you run since Lion.. all have the airport utility installed by default and will look much the same.

If you are having issues make sure the mac is linked to the airport wireless and not the belkin.

If it still doesn't work plug in by ethernet and change the airport utility over to using ethernet instead.. this is much better anyway.

In other words, I seem to have two networks running at the same time.

Correct, based on the information that you have provided. If you want to have only one network, then the Extreme will need to be set up to use the same wireless network name and password as the Belkin.  Then, the Express will need to be reconfigured to extend the Extreme network.

But, this won't make much sense unless you have the Extreme located a few rooms away from the Belkin.....since you would not want to have two devices in close proximity both producing the same network.

Not sure if the Extreme and Belkin might be competing for a channel?

Assuming that the Extreme and Belkin are working correctly, they will each choose a different channel....automatically.

I am trying to extend my network (we have some kind of interference from the top floor to the basement) by using the AirPort units as extenders

That can be done, but both the Extreme and Express will need to connect back to the Belkin router using a permanent wired Ethernet cable connection.  The Extreme and Express cannot wirelessly extend the Belkin network.

I had been using the Extreme as the base router but, for whatever reason, it began dropping the connection to the modem

What model number of Extreme?

How old is this device?