OK, here's a test setup for the CD4046B that you can build up on breadboard or stripboard to get an idea of what it does and whether it will be useful to you.
The VCO in the 4046 is a voltage controlled oscillator. This means that it generates a signal (a tone) at a frequency that is determined by the control voltage on pin 9, in conjunction with the other frequency-setting components: C1, R1+VR1, and R2+VR2 (if JP1 is closed).
For your application, I've chosen a C1 value of 22 nF (nanofarads), which I think will enable you to operate the VCO over an appropriate frequency range: around 8~12 kHz.
This is within the frequency range that's audible to humans, and can be acquired by a standard sound card through the line input. (Don't use the microphone input.)
The reason for using frequency modulation (instead of connecting your heartbeat monitor directly to the sound card input) is the very low frequency of the heartbeat signal. Sound cards aren't normally designed to acquire signals below around 20 Hz but heartbeat signals are around 1 Hz, and to reproduce them properly you really need a frequency response that extends below 1 Hz.
You need some way of converting the heartbeat signal into a signal that can be easily and acurately acquired by the sound card - something comfortably within the frequency range that the sound card is designed to acquire.
You will need to do some experimenting to get a reasonable frequency range for the signal that your "input processing circuitry" generates. That's why I've suggested preset potentiometers (aka "trimpots") for the R1 and R2 components. You may also want to get a selection of capacitors to try for C1 - for example, 4.7 nF, 10 nF, 47 nF and 100 nF as well as the 22 nF value I suggest.
The frequency accuracy of this circuit will depend on a number of factors. I've specified C1 as having an initial tolerance of ±3% and this type also has a typical drift with frequency of only around ±1% from -40°C~+60°C, so it's relatively stable. The 4046 is affected by temperature, but I don't know how much. The resistors and trimpots have a guaranteed temperature coefficient of resistance of ±100 ppm/°C (0.01%/°C) which is fairly stable. The power supply voltage will also affect the 4046 and it must be regulated; the exact value is not critical.
Any variation in the no-signal DC voltage from the input processing circuit will obviously also affect the output frequency as well. If you upload a schematic of this circuit, I may be able to advise you. The no-signal DC voltage from the input processing circuit needs to be comfortably within the supply rails; ideally, around half the supply voltage would be best. In this case you won't need R2+VR2, so you can leave JP1 open. You may need R2+VR2 if you want to reduce the VCO frequency range.
The CD4046 data sheets claim that the VCO is "highly linear" but that's not entirely true, especially with lower values of R1. In other words, the frequency you acquire with the sound card will not necessarily map linearly to the voltage coming from the input processing circuitry.
Other components are not critical at all. CD and CC can be cheap ceramic capacitors. RA and RB form an attenuator to reduce the amplitude of the VCO output (which swings from 0V to the positive rail) down to a level that the sound card should be able to accept on its line input.
If you have a multimeter that measures frequency, this will simplify your testing and setup a lot. Connect it to pin 4 of the CD4046. You can also connect the output (on CN1) to an audio amplifier while you make adjustments; this will give you immediate audible feedback on any adjustments you make.
Use the highest sampling frequency available; at least 44.1 kHz. This will ensure a reasonable number of samples per cycle of the VCO signal.
For testing, you can use an audio recording program such as Audacity. To use it for real-time acquisition and analysis, you will need to write software that talks directly to the audio input driver and analyses the frequency in real time. Assuming you want to be able to do that.
Have a think about this, and if you think it's worth trying, build it up and have a play around with it, to get a feel for what it does and how you might be able to use it.