Is this a totally dysfunctional way to go about finances in a relationship and am I right to be a bit fed up with it?

[Frombathwithlove]

This will probably be a bit lengthy, so you might want to grab a coffee!
So, the basics are: DP and I have been together 7 years and live together in a rented house. Both married before, my 2 DC live with us and DP's 2 children live with his ex and her partner. DP works full time and I work part-time (at least 30hrs/wk spread over 3 jobs). I receive maintenance from my ExH and DP pays maintenance to his ExW. I also receive child benefit for DC's.
That's the basics! The rub is this; DP and I pay 50% each of rent & joint utilities. We pay our own individual bills independently (i.e car insurance, credit cards, pension, catalogues etc and we run a car each). We have separate personal bank accounts that our wages go in to - mine also has CB and maintenance going in to it - we have a joint 'bills' account that we pay our 50% in to and the direct debits go out of that.
Alongside this, I fully support my dc with EVERYTHING! From clothes to school trips to Christmas & birthday presents. On their birthdays we all go out for a meal and I pay. DP earns approx. £10,000 pa more than me , he pays maintenance for his dc (as mentioned before) and sees them for 1 day every weekend. If DP, my DC and I go for a coffee/lunch when out, I pay. I buy all the necessary things needed for the home (decorating, furniture when needed, soon to be flooring & carpets too). We also pay an amount in to the joint account to cover food, 50/50 again - it never covers the cost of food though, I always have to add to it.
So, the whole 'separate the finances' came about a few years ago when DP was moaning about what I prioritised when it came to money. I got really cross and worked a ratio of what we should pay, along the lines of: he earns x % more so should pay more (I know that sounds arsey, but it was how I felt). DP didn't like the ratio and said that there were 3 of us (me & DC x2) and only 1 of him so why should he pay more? He said it wasn't happy with it and agreed 50/50.
So, here we are. I feel like a single parent within a relationship! But, actually worse off than a single parent; because if I was truly on my own I would get assistance from the DSS!
Would this annoy/upset you?
(In fact, is it so garbled that you lost the plot ages ago?!)

@Chasingsquirrels
Sorry you and DH have had such sad news. That puts my complaining in to some perspective. You are right though, I am more upset than anything else. It is hard for me to accept that DP can see me struggling with finances, but feels it ok to continue.
@SheldonCRules
All well and good if DP is saving a nest egg for his DC, a responsible Father is to be commended. However, he always goes under the guise of step-father to my DC (his choice of name) and I have difficulty keeping up with their here and now provisions in the current situation.

It's ridiculous if you love a mother you love the dc and that includes financially supporting them. Why are you allowing him to rest you dc like this op?

Treat.

I think him saying there's three of you and one of him would have fucked me right off. Are you not a family then? You shouldn't be having to pay to top up the food account etc... on your own.