Well this is terrible, and I feel really bad for you. That HR are not warm and fluffy is not a surprise to me, but this goes beyond that into true asshole.
Get you, or your partner, to send an e-mail to her stating that you miscarried on x date, and have found the experience stressful and distressing, and that you felt her comments were unhelpful in what is a serious and traumatic time.
Explain that it is entirely reasonable (and state this as fact, because it is fact and all the employment tribunals and best prcatice guides will back you up) to request compassionate time as well as sickness absence in order that you are able to return to work effectively. State that that you are not in a position to confirm the details until you are aware of how much this has affected you (but give them a guideline eg, I will contact you in .. to confirm (make sure this is more than reasonable - too often in the early stages of anything like this, people over estimate just before the real trauma hits and then miss their own deadlines -- you need to guard against this),
Finish with a 'understand the need for business continuity, so you would ask for any specific immediate concerns to be conveyed to you (by e-mail) and that you will answer on or before (timescale above).
Its sad, but you need to mention trauma, distress etc and that her comments were unhelpful specifically otherwise they will claim they didn't know that a miscarriage has been traumatic for you 'because you didn't say' - ridiculous but true. You need to also get these words down as they ring gentle bells in hR minds that you aren't lying. Putting it in writing early is key and this is the most important thing.
Copy your reply to your manager (as they will need to know), the HR rep you spoke to, and to her manager so that she is aware that you are gently and understandingly unhappy with her ignorance over this issue.
Aside from all that, this must be awful for you and I hope that you and your partner will be forgiving of any below the radar effects - a friend of mine miscarried, and she felt lost and confused without realising it for some months Hang in there and lean on us and pals - they will appreciate the chance to help even if its leaving you alone, or just being there...