I sympathise. I our region of Scotland, each household has 4 wheelie-bins, a thin, half volume one for landfill (collected every 2 weeks), and 3 normal-sized wheelie-bins for paper/card (every 4 weeks), cans/plastic (every 4 weeks) and food& garden (every 2 weeks).
I have a half-acre garden (rural, so not unusual to have large gardens), and can hide the bloody things behind a hedge, but the village/town houses with less space look a mess with bins everywhere and often left in the street for days at a time blocking pavements, and it's a right PITA to remember which bin to put out, and when. No bin will be emptied if the lid is even 1/2 cm open, no extra bags will be lifted. You can't buy extra bins, or extra collections.
There is no glass collection, so on a weekly basis, we have to drive around 5 miles to the dump (or 6 miles to the supermarket), sorry recycling centre with the glass and with the plastic, cans and paper and card as the bins for monthly collection are full in about 10 days.
My kitchen and utility room are typically full of empty cartons etc soaking/drying (it has to be washed!), or waiting to be sorted..... I hate washing it all, PITA and bugs the hell out of me.
There is absolutely no capacity in the land-fill bins to put in ANYTHING such as glass (which our council refuse to recycle), as we have a baby + 5 other people in the household.
We get the same allocation of recycle bins as 1 or 2 person house-holds, and that appears to be what the council have based the collection needs of the "average family" on. Everyone I know with more than 1 child seems to do the same - take car boots full of recycling with them to the supermarket as the do not have room in their recycle bins.
The obvious answer here would be fortnightly collections, not monthly. We have noticed an increase in "fly-tipping" in fields/gateways/rural roadsides, since the new 4-bin-scheme was put in place about 18 months ago.
I get heartily sick of it all, and am envious of my mums region of Scotland, where everything goes in one bin (there are bottle/can banks in every village), and the binmen will lift extra bags. It is all sent to a central mechanical sorting centre and the residue goes to a power plant. None to Landfill.