You will invariably level more than one class/job in Final Fantasy XIV, as utility is often the most desired asset when searching for party members. Before the servers for 1.x did their final save, I had white mage, black mage, and bard at level 50. Dragoon was next on my list, and I had already purchased gear for it.

To be clear, there is no hybrid black mage and white mage. There is, however, the opportunity for a hybrid thaumaturge and conjurer. The difference between classes and jobs in Final Fantasy XIV is that classes may borrow abilities from all other classes. This allows them to be more versatile, and allows them to lean toward jack-of-all-trades by supplementing a class's weak points by borrowing from other class skills (for example: thaumaturge using stoneskin, protect, and cure from conjurer to supplement their offensive spell repertoire). This is more useful in solo or small-group situations where you will need to fulfill multiple roles.

Jobs, on the other hand, are specializations of each class. Black mage is geared towards optimizing a thaumaturge's damage output by offering higher base intelligence and magic attack potency as well as additional, more powerful spells (freeze, flare, burst). This specialization allows them to better fulfill a set role (magic damage dealer) in group situations. The trade off for this specialization is that the number of classes from which a job can draw additional talents is limited to two predetermined classes. Black mage, for example, can only borrow abilities from archer and pugilist. As a consequence, the customization of jobs is significantly lessened by comparison. Consequently, most people will use the same cross-class abilities which compliment their job's specialized purpose. Take, again, black mage. You will almost always set Quelling Strike and Chameleon (both abilities from Archer that are useful for enmity mitigation) and Featherfoot and Second Wind (two support abilities from Pugilist useful to survivable in oh-trout situations). There is very little deviation from this as, for the most part, the number of useful cross-class abilities available to any given job are notable fewer.

All job specific abilities are exclusive to each job. Unlike class abilities, they may not be borrowed and are only available when that job's soul stone is equipped. While the specifics of this system are changing in A Realm Reborn (specifically, the list of abilities for each job has been drastically overhauled), the core mechanic is expected to remain the same. Classes will be flexible and able to borrow abilities freely from other classes. Jobs will be specialized to a specific purpose with flexibility and utility as the trade-offs. Note: not all class abilities are available to every class. Conjurer's cura, for example, requires conjury. While other classes may borrow cure, they may not borrow the stronger version. Expect this to remain a feature as well.

In case you were curious, white mage's classes are pugilist and gladiator, so they are unable to borrow class abilities from thaumaturge to do the same thing in the other order. I'm hoping the introduction of arcanist and summoner allows for a Disciple of Magic that can actually use abilities from the other magic classes while in a job.

tl;dr - Cross-class hybrids exist. Cross-job hybrids do not.