There is a big difference between overhead rated (ACSR) triplex and underground-rated triplex or quadplex (typically type USE).
It"s not the triplex/quadplex that"s the issue; its the overhead-rated nature of the triplex the original poster posited.
Overhead rated triplex has thin insulation befitting use in free-air and a steel center wire on the messenger that makes the wire strong enough to hang from poles. Underground rated triplex/quadplex has thick insulation for use in continuously wet locations (not to mention direct bury) and a plain-vanilla aluminum ground/neutral.
Underground triplex is still bulky, but it is much more flexible, and can be pulled through (big enough) conduit. Most of my objections to using "triplex" in an attic (or in conduit) disappear if we are talking wire not rated for overhead use. It"s entirely possible that the installations described by John T and George Marsh were completely code compliant (I"m a little unsure on the code compliance of USE inside buildings for a building to building feeder application.)
But it is clearly fine to enclose it in conduit for a service entrance emerging from the ground, and there may in fact be no other way to do it (it must be protected from physical damage inside buildings.)
But the original poster was pretty clear that his triplex was overhead-rated, and it would be pretty wrong to say that there"s no issue with that.
One more note: electric utilities are regulated by their own code; NOT the National Electrical Code. It is assumed that utilities employ electrical engineers to supervise the processes that they use for distribution.
No such assumption is made for commercial/residential wiring, and the NEC is more conserviative.
The dividing line between utility rules and NEC rules is the "service drop" for an overhead installation (basically the drip loop and splices up on the roof). For an underground installation it is the electric meter or service disconnect means.
In general, overhead-rated triplex is stuff used by utilities, and that"s one reason there"s not much (if any) discussion of it in the NEC.