Your question and DoubleAA's comment on my original answer have inspired me to do some research and learn some really fascinating information about the Hebrew calendar.
First, some background information:
Our current 19-year intercalary cycle was instituted by Hillel II in the fourth century CE. The calendar is a lunisolar calendar which typically has 12 months. A normal year is 354 days, which is approximately 11.25 days shorter than the solar calendar. To correct for this, the Hebrew calendar has a leap year every 2 or 3 years for a total of 7 times every 19 years. In those leap years, instead of a single day (which we add to our solar calendar), an entire month is added.
Now your question:
According to Wikipedia, at the time when the calendar started, the earliest Passover (corresponding to the 16th year of the 19-year cycle) fell on the vernal equinox and Passover always fell on the first full moon following the equinox.
Over the centuries, there has been a very slight seasonal drift in the calendar (the average year is just over 6.5 minutes longer than the Gregorian calendar). As a result, the calendar has shifted about 7 and a half days later relative to the equinox. But since the months themselves cannot be shifted by a full week (since the new month is tied to the new moon) the result is that in certain leap-years, the leap-month which is supposed to correct for the drift is inserted a year earlier than it should have been to actually match the equinox. This currently happens in the 8th, 11th, and 19th years of the 19-year cycle. Basically, in those years, there has been one more leap year than there actually "should have been" between the fourth century and today.
As you mentioned, this year Passover is not on the first full moon following the vernal equinox. That is because, this year is the 19th year of the current 19-year cycle, which is one of the years where the leap-month is added "prematurely". At this point, there is not much concern about Passover occasionally falling out on the second full moon after the equinox. There is no requirement in the Torah that it fall on the first full moon. There is, however, a requirement that Passover must fall in the Spring (it is called the Spring Festival). If the current calendar were to be followed indefinitely, Passover would eventually fall in the summer due to continued seasonal drift. This would be problematic, but it is not of immediate concern because it would take millenia for this to happen. The hope is that the messiah will come well before then and re-introduce the court-based institution of the months and leap years.
Some bonus information:
You may have noticed that I mentioned that our current calendar was instituted in the fourth century. Of course, the time period that Christians are interested in occurred before this time. Prior to the establishment of the fixed (calculated) calendar, the leap years were determined by the courts. The main factors that the courts took into account was the relationship between Passover and the equinox. They needed to make sure that Passover always fell after the vernal equinox. In addition, however, they could consider other factors that affected the ability of the people living throughout Israel to properly observe the Pesach festival. If the winter rains had destroyed the roads and bridges (which would prevent people from far away from making the festival pilgrimage) or they had destroyed the ovens for roasting the paschal sacrifice, the courts could institute a leap year in order to allow an extra month for the roads and ovens to be fixed before the festival (see Rambam - Mishneh Torah, Kiddush HaChodesh, Chapter 4, Halakha 5).
In a year which was declared a leap-year for one of those reasons, it is entirely likely that such an additional month would push Passover to the second full moon following the equinox. So even before the set calendar and seasonal drift, it was possible for Passover to fall out not on the first full moon. I am not aware of how often this happened (if it ever actually happened at all), but it is most likely (in my opinion) that Passover did occur in the first full moon following the equinox (as it does in most years now and probably in almost all years back then) in the year Christians believe Jesus was killed .