All Moultons have had front and rear suspension since 1962.
My 1965 Moulton Stowaway 2 speed with coaster brake [the F-frame model mentioned above] surprises everyone who rides it with its comfort, load carrying and real bike handling. My Moulton Mark III from 1973 the next evolution for Moulton is also a treat to ride with 3speed SA hub with drum brake. My 1988 Moulton ATB is the space frame version mentioned and designed for off road riding and touring. It too is a surprise to those who see it and ride it particularly off pavement on single track.
http://mombat.org/1989_Moulton_ATB.htm
The current models that I would suggest for touring include the Bridgestone Moulton. An aluminum frame designed by Moulton and built by Bridgestone with an updated suspension design. Price $2K+; Various Pashley built Moulton APB's[All Purpose Bicycles] are similar to the ATB I had but at a lower price point; Most models separate but do not fold which helps for transport to touring destinations.
http://www.sheldonbrown.com/audacious.html#1 An APB rides the PBP [Paris-Brest-Paris]
For touring on older and current models see:
http://http://www.greenbicycle.com/ or
http://www.moultonbicycle.com/
The hand made high end Moulton models have an incredible suspension, handling and load capacity for touring as well but at a significantly higher price point depending on the $ vs £. reaching $13-15K at one point recently for the New Series Double Pylon model as I recall.
http://www.bikeradar.com/gear/catego...78#review_body
Otherwise go to the moulton site.