There exist many acceptable options as a Minotaur Battlemind multiclassed into Monk. While it's not a full hybrid, it's possible to strongly evoke monastic traditions in your action descriptions, your utility powers, your skills, and your paragon path. This makes you a charge-focused damage-dealing defender who can hold their own with most characters.
A bit of a discursive deconstruction here, riffing off my paper.
First: literature reserach. Do there exist any battlemind or monk hybrids?
Do there exist any published multiclass builds that use either?
No, not really.
Now we... must be creative.
In general, when doing a risky combo like this, you can't afford to slip up too badly. Read both class guides battlemind monk to get a sense of appropriate powers. In all cases, take the mechanics of the powers and choose your description for yourself, starting with their name. Steal all names from ancient martial arts moves and be unusually aware of the environment and ways to perform acrobatic manoeuvres while establishing your battlemind as the centre of attention.
Narrative requirement: we must have a minotaur, involve the idea of "monk" and the idea of "battlemind."
Mechanical-functional requirement: we must function as a character.
Primus, there exist no mechanical options for hybrid stats, save for a joint (and unimportant secondary.) Monks are Dex/Wis or Dex/Str, Battleminds are Con/Wis or Con/Cha. Minotaurs are Str Con/Wis.
Monks have a huge reliance on their secondaries. Battleminds have less.
Therefore, is it possible to make a Con/X? battlemind that is heavily invested in monkishness?
Minotaurs are chargers, and there are a number of battlemind charge options that are ... not bad. Momentum Swing as a 3rd level give us an augment 2 charge, which really ties in nicely with a charge chassis (to be a striker) and the minotaur's natural gifts.
There are a number of excellent statless stances from the monk. Most notable being centered defense (utility/6) or other utilities. The monk's positioning utilities synergize wonderfully with the Battlemind's interrupts, especially if flavoured as monastic training rather than psionic power.
At 7, we'll choose forceful reversal as an indication of a judo or akido like form of literally turning the force of the enemy's attack on them, and focus a little more on forced movement.
While we won't choose a daily or encounter multiclass, the utility flavouring as well as the ki-focus should be a nice start. There's even a perfect monk paragon path: Soaring blade. Its abilities are constitution focused, and it gets bonus damage... equal to con... on all melee attacks at 16. Its bonus to acrobatics means that you can even pretend to be a monk somtimes when doing dexy stuff.
So, in heroic, we have a minotaur charger, focused on the augment 2 charger. Your weapon is the sword, echoing your paragon path. (Theme this as your monastic weapon) First feat is Monastic Disciple, to get your iron soul flurry of blows. Choose an appropriately monky theme. You'll want a very high strength to power your basic attacks, which... isn't very good from a theoretical perspective, but survivable.
Equipment is generally the charge chassis, which must be reflavoured not as ubermagicitems, but as monastic tricks to make your damage more interesting. I urge you to grab a book on aikido and Kenjutsu and theme all your attacks appropriatly. Throw in a hint of tai-chi, just becuase it's appropriate to explain your elemental effects.
You'll want to grab the utility multiclass into monk, and the monk PP.
That provides a solid defender who is focused on doing damage and is themed around being a "monk." Your heavy armor focus is a touch unfortunate, but my recommendation is to accept it, and just call it unusually heavy robes.