Power-Supply "Combination": Solar for voltage + Battery for current
Don't even think about creating the setup you just described. It is bloody dangerous.

If you wire the "solar cell pack" and the two battery packs in parallel without connecting the Raspberry Pi, you'll get a loop. Kirchhoff's second law explains that the sum of voltages around a loop must be zero. In this case, if you start going around the loop in one direction, you'll encounter the two power sources with opposite directions, so now their difference must be zero - so they must be at an equal voltage. Will this be 6V (dictated by the solar panels) or 3.7V (dictated by the battery packs)? The following will happen:


Initially, without sunlight, the common voltage will be 3.7V. No current flows, since the solar panel does not let current flow backwards (its resistance goes near infinity). All is well for now.
Then you apply sunlight. The solar panels try to increase the voltage to 6V, but at this voltage the batteries would allow through much more current than they can supply. So the panels drop their voltage to 3.7V, but still begin to charge the batteries with the couple hundred milliamps they can supply, until the voltage in the battery packs reaches 6V. And there's a pretty good reason the batteries are rated at 3.7V.
If I learned anything about Li-ion and Li-polymer batteries is that they are very easy to upset. And they especially don't like being overcharged. If they are indoors, they will blow up your desk and burn your house down. If they are oudoors, they'll happily ignite the grass around them. Then burn your house down. Li-ion and Li-polymer batteries are not toys. Don't even think about putting them in a circuit where there's even a slight chance they'll get overcharged.


Connecting the Raspberry Pi before the detonation wouldn't work out well either. The 3.7V combined power supply is not enough for the Pi, which will then do one of the following (I'm not familiar with the Pi's power supply circuit):


Pull a lot of current overheating the battery, the solar panel and maybe even its own on-board voltage regulator. It will not boot, or even if it does, it will frequently crash and reboot because of the inadequate voltage. This goes on until one of the components fail: if it's the solar panel, you're safe. If it's the Pi, it's the time bomb scenario all over again. The battery packs also don't like being over-discharged, but as far as I know, they don't burst out in flames then. They just don't work anymore.
Don't pull any current at all. Then it's like you didn't connect it at all. Time bomb again.


Creating a circuit which safely combines solar and battery power requires advanced electronics skills and dedicated circuitry. In your case, I would follow S.J. Becker's advice (+1) and buy a (solar powered) power bank from eBay. The circuitry is there, pre-made for you and it can power your Raspberry Pi longer than your setup would have even if it worked. I know they are not as cheap as using things from your parts bin, but they are definitely cheaper than replacing your burnt furniture.

Additionally, does the thing have to be solar powered?

Edit: Some battery packs have built-in protection circuitry that shuts the power off if the battery is overcharged, so there's a chance your setup won't actually ignite but just not work at all.