advice sought for double paired design

Dear mixed modellers,

just want some opinions from those willing to share them - I have a design 
and wonder if mixed models could analyse it.

*I have 34 sites that are split into pairs of sites that do or do not 
receive a treatment. This means I have n=17 as the pairs are obviously not 
independent of each other.
*I surveyed information from them also _before_ and _after_ treatment was 
applied so each pair/site is also paired over time due to the repeat 
measurement. *With each survey 2 repeat measurements were taken 
simultaneously over 2 habitats.

I was wondering if this is a reasonable design to tackle with mixed models? 
I have researching matched pairs designs but they fail as there is the 
double pairing non-independence issue. I am interested in whether or not 
treatment affects y, and not how site A at time 1 is different to site A at 
time 2 - there is a seasonal issue so I know it will be different. 
Treatment is my key question, and if the 2 habitats are affected 
differently. My limited knowledge of mixed models tells me it is doable but 
I want to check with people that really know what they're talking about!

If in theory mixed models are suitable, would a design like this be 
appropriate or will it need to be a little more complex that this super 
simple model?
lmer(y~Treatment+Habitat+(1|Site)+(1|Treatment)+(1|Period)+(1|Time), data)

Any hints you could give me would be gratefully received.

Kate

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Ph.D student and mixed model beginner